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Question
Using componendo and dividendo, find the value of x
`(sqrt(3x + 4) + sqrt(3x -5))/(sqrt(3x + 4)-sqrt(3x - 5)) = 9`
Solution
`(sqrt(3x + 4) + sqrt(3x -5))/(sqrt(3x + 4)-sqrt(3x - 5)) = 9`
Using componendo and dividendo,
`(sqrt(3x + 4) + sqrt(3x - 5) + sqrt(3x + 4) - sqrt(3x - 5))/(sqrt(3x + 4) + sqrt(3x - 5) - sqrt(3x + 4) + sqrt(3x - 5)) = (9+1)/(9-1)`
`=> (2sqrt(3x + 4))/(2sqrt(3x - 5)) = 10/8`
`=> sqrt(3x + 4)/(sqrt(3x -5)) = 5/4`
Squaring both sides,
`=> (3x + 4)/(3x - 5) = 25/16`
`=>16(3x + 4) = 25(3x - 5)`
`=> 48x + 64 = 75x - 125`
`=> 75x - 48x = 64 + 125`
`=> 27x = 189`
`=> x = 7`
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